you just want to find that balance between heals and DPS. Depending on the class you are playing you will have different kinds of skills but what I find with WHM is with stoneskin up and eye for an eye I have quite a lot of time before the Tank is in any real danger so I can start in cleric stance and pump out some DPS. At 60 the rotation changed a bit so I go something like open with holy which will stun all mobs and damage them meaning the Tank is taking no damage, Aero III which will hit all the mobs then holy again for another stun, assize gives you mana damages all mobs with possible big crits and gives some HP back to the Tank then a final holy if you can before cleric stance is turned off and Tank is topped up. By that time everything should be dead anyway with good DPS you will barely need to heal the Tank.
Synergy with another Healer is hard in a PuG you don't know each other or how you like to play your class. There are several accepted rotations for Tank and DPS but with Healer often people just throw their own playstyle in so it can be hard to learn what kind of person you are playing with. Depending on the class the other Healer is and how they play I try to adjust my style a bit. Some Healers will heal a ton so you can heal a bit less off their shoulder and do DPS at the same time though this suits a SCH more so if you are WHM and the other person is a SCH I'd just assume they want to do that so take on the power Healer role and pump out heals. SCH can handle mitigation and DPS quite easily as can AST and are good at focusing on a single target like the MT leaving the WHM to focus on big group heals for raid wide damage and spreading their HoT.
For the most part it's about knowing what the class and the player are good at and trying to make the most of their skills and how they fit in with yours.
I think I play better when I have more of a free role to get Healing to areas that need it most and get a bunch of DPS out but I'm quite comfortable doing heavy healing too.